If we play with it a bit, we see the absurdity of this need to protect our psychological selves. This seeing does not expand our territory, in fact it shrinks it! It happens when we are alert and attentive, and it has the same quality and energy as when we hold a question without looking for answers. As mathematicians we are often told: if you really understand a problem, then the answer lies in it. It appears to me that the key to understanding ourselves lies in this ability to ask questions of our inner world, without judgment or defence, and without settling on answers.

AtRiA, November 2019 focuses on journeys -some are enjoyable, some tiresome, some endless. A mathematician’s journey is full of unexpected delight, simply because of unexpected detours, sudden discoveries and interesting alternatives. Have fun as you travel with us. Read all about the young Yatris and their journey of discovery in Features. This section also describes more abstract journeys from the Regular Pentagon to the Icosahedron and the Dodecahedron (Part 2) and from the familiar 2 and 3 dimensions to n dimensions in Extension of the Pythagorean Theorem. In ClassRoom, Simple Cryptography and Triangles with Integer Sides are articles sparked off by previous articles in AtRiA . An Unusual Proof of the Centroid Theorem, Modified Pascal Triangle and Orthocentre of a Triangle may motivate you to write similarly! You will find ideas in our regular columns – How to Prove It, Low Flow High Ceiling and TechSpace which features the simulation of a dice game this time. Our issue is short of 100% without the PullOut, enjoy the learning trajectory on Percentages, defined and illustrated with plenty of examples in this issue. How Craig Barton Wishes he’d Taught Maths is an excellent review by Sir Timothy William Gowers, reprinted from his Weblog. If not yet subscribed for hard copy send in your brief profile and postal address to AtRightAngles@apu.edu.in and do share your feedback at AtRiA.editor@apu.edu.in

Lazy summer afternoons spent playing endless games of Sutli or hopscotch or any of those absorbing games have often become the topic of endless reminiscing about the good old days. Well, let’s bring them back! With a math slant at that. Can the shapes made with knotted string lead to a better understanding of Euclidean geometry and 3 D space? Can the mobiles which hang over a baby’s crib be used to understand how to solve equations? Can a teacher see how easy it is to reinvent a toy or a game in order to teach a mathematical concept or two? It’s time to Deja View mathematics!

The word ‘heuristics’ has always left me fumbling for the perfect definition. Rule of thumb seems adequate but too informal, as a teacher trainer, I’ve always preferred to illustrate rather than define this word. And the first article in the November issue does just that- Gaurav Bhatnagar, leads you gently into the Exponential Series- a heuristic definition! The relaxed tone continues with V. G. Tikekar setting the stage to arrive at formulae which are usually given and proved using mathematical induction. He, on the other hand, uses the narrative mode to set the context which explains and then proves the sum of squares and sum of cubes formulae. From story we move to song, V. Ramprashanth’s article Tonic Ambiguity is a delightful depart from our usual articles and it explains very simply, using just the concepts of ratios, how two hearers can place the same tones at different positions on the musical scale. CoMaC and then Shailesh Shirali, wrap up the Features section with a bouquet of proofs.